A certain sum of money is invested in a business. in each year this investment earns 1 1/2 times as much as in the preceding year. If the investment earned a total of $29,250.00 in four years, how much did it earn in the fourth year?
amount= origamount*1.5^timeInYears
so in four years, amount=orig*1.5^4
earned=amount-orig=orig^1.5^4-orig
29250=orig (1.5^4-1)
solve for orig, then
then solve for amountafter4years, and amount after three years, and subtract.
amounteared4thyr= orig(1.5^4-1.5^3)
= orig (1.5^3)(1.5-1)
thanks
1. A sum of money is invested in a business. In each year this investment earns 1 times as much as in the preceding year. If the investment earned a total of $29,250 in four years, how much did it earn in the fourth year?
• CORRECT: $12,150
How to get it is to find out the original investment and do that by the following steps
amount= origamount*1.5^timeInYears
so in four years, amount=orig*1.5^4
earned=amount-orig=orig^1.5^4-orig
29250=orig (1.5^4-1)
29250=x(1.5^4-1)
Let's solve your equation step-by-step.
29250=x(1.54−1)
Step 1: Simplify both sides of the equation.
29250=4.0625x
Step 2: Flip the equation.
4.0625x=29250
Step 3: Divide both sides by 4.0625.
4.0625x
4.0625
=
29250
4.0625
x=7200
Witch is 7200 then times it by 1.5^4 then
7200(1.54−1.53)
=(7200)(1.54+−3.375)
=(7200)(1.54)+(7200)(−3.375)
=36450−24300
=12150
To find out how much the investment earned in the fourth year, let's work through the problem step by step.
Let's assume that the amount of money invested in the business in the first year is x dollars. According to the problem, in each subsequent year, the investment earns 1 1/2 times as much as the preceding year.
So, in the first year, the investment earns x dollars.
In the second year, it earns (1 1/2) * x = (3/2) * x dollars.
In the third year, it earns (1 1/2) * (3/2) * x = (9/4) * x dollars.
And in the fourth year, it earns (1 1/2) * (9/4) * x = (27/8) * x dollars.
Now, let's set up an equation to represent the total earnings over the four years. We know that the total earnings over the four years is $29,250.00.
So, we have the following equation:
x + (3/2)x + (9/4)x + (27/8)x = 29,250
To simplify the equation, we need to find a common denominator for the fractions on the left side:
8x/8 + 12x/8 + 18x/8 + 27x/8 = 29,250
Combine the terms on the left side:
(65x/8) = 29,250
To solve for x, multiply both sides by 8/65:
x = (29,250 * (8/65))
Calculating this, we find:
x ≈ $3,600.00
Now, to find the earnings in the fourth year, we substitute x back into the equation:
(27/8) * $3,600.00 ≈ $12,150.00
Therefore, the investment earned approximately $12,150.00 in the fourth year.